CN112198052B - Method for calculating tensile strength of rock under confining pressure condition and application - Google Patents
Method for calculating tensile strength of rock under confining pressure condition and application Download PDFInfo
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- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N3/08—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
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- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0001—Type of application of the stress
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- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0014—Type of force applied
- G01N2203/0016—Tensile or compressive
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- G—PHYSICS
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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- G01N2203/0019—Compressive
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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- G01N2203/0067—Fracture or rupture
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
- G01N2203/025—Geometry of the test
- G01N2203/0256—Triaxial, i.e. the forces being applied along three normal axes of the specimen
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
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Abstract
The invention discloses a method for calculating the tensile strength of a rock under a confining pressure condition, which calculates the tensile strength of the rock according to a relation criterion of the confining pressure and the tensile strength of the rock. The method comprises the steps of S1, carrying out tensile tests on the rock sample under different confining pressure conditions, and obtaining the tensile strength of the rock sample under different confining pressure effects; and S2, performing data fitting according to different confining pressures and corresponding tensile strengths thereof, determining constant values related to the properties of the current rock material, and calculating the tensile strength of the current rock under different confining pressure conditions according to the determined relation criterion of the confining pressure and the tensile strength of the rock. The relation criterion of the rock confining pressure and the tensile strength, which is provided by the method, provides a basis for rock fracture identification, provides a comparison reference for judging rock fracture through the tensile strength, and provides a theoretical basis for stability control and instability early warning of an engineering rock body.
Description
Technical Field
The invention relates to the technical field of rock mechanics research, in particular to a method for calculating tensile strength of a rock under confining pressure and application thereof.
Background
Rock tensile failure is often encountered in the construction of most rock engineering, such as tunnel excavation, underground cavern construction, high and steep slope unloading, mining and the like. Rock fracture often accompanies great ground stress in-process, and the rock is promptly received confining pressure, and tensile failure under the complicated ground stress condition is often more violent, once handling the mistake, is likely to cause construction progress delay and to cause the damage to personnel's equipment etc.. At present, the rock fracture process is generally equivalent to pure uniaxial tension failure, and the rock is neglected to be subjected to confining pressure in the actual environment, so that the tensile strength of the rock under the confining pressure condition needs to be deeply researched.
At present, the research on the tensile strength of the rock under different confining pressure conditions is less, and the rock tensile failure strength change under the confining pressure action cannot be predicted without a universal relation criterion between the confining pressure and the tensile strength.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a method for calculating the tensile strength of a rock under a confining pressure condition for application.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method for calculating the tensile strength of a rock under a confining pressure condition is characterized in that the method calculates the tensile strength of the rock according to the relation criterion of the confining pressure and the tensile strength of the rock of a formula (1);
wherein σ3As tensile strength, σ1Is the confining pressure value; m, n, k, q and a are constants.
The method comprises the following steps:
step S1, performing tensile tests on the rock sample under different confining pressure conditions, and acquiring tensile strength of the rock sample under different confining pressure effects;
and step S2, performing data fitting according to different confining pressures and corresponding tensile strengths thereof, determining constant values related to the current rock material property in the formula (1), and calculating the tensile strength of the current rock under different confining pressure conditions according to the determined relation criterion of the rock confining pressure and the tensile strength.
The process of the tensile test in step S1 is:
1-1, preparing a rock sample, wherein two ends of the rock sample are respectively bonded with a metal end with a threaded hole;
1-2, vertically installing a rock sample on a tension-compression conversion device, and fixedly connecting metal ends at two ends of the rock sample with connecting ends at the upper part and the lower part of the tension-compression conversion device; then integrally sealing the tension-compression conversion device provided with the rock sample in a confining pressure cavity of a three-axis compression testing machine, wherein two loading heads of the three-axis compression testing machine are fixedly connected with a loading end of the tension-compression conversion device respectively, and filling silicone oil into the confining pressure cavity;
1-3, applying confining pressure to the rock sample, and gradually applying axial pressure to the rock sample after the confining pressure value is stable; when the rock sample breaks, the stretching is stopped.
The rock sample is made of granite and is a cylinder with the height of 100mm and the diameter of 50 mm.
The invention also provides an application of the tensile strength calculation method of the rock under the confining pressure condition, which is characterized in that a tensile test of a rock sample is required to be performed in advance, and values of m, n, k, q and a corresponding to different rock materials are determined; measuring the confining pressure value of a rock at a certain position, and calculating according to the relation criterion of the formula (1) to obtain the theoretical value of the tensile strength of the rock at the position when the rock is broken;
monitoring the actual strength of the rock at the position in real time, and when the actual strength of the rock is smaller than the theoretical value of the tensile strength, indicating that the rock is not cracked, and continuously excavating; when the actual strength of the rock is greater than or equal to the theoretical value of tensile strength, the rock is cracked, and the excavation operation needs to be stopped.
Compared with the prior art, the invention has the following beneficial effects:
1. the relation criterion of the rock confining pressure and the tensile strength provided by the invention provides a basis for rock fracture identification, provides a comparison reference for judging rock fracture through the tensile strength, and provides a theoretical basis for stability control and instability early warning of an engineering rock body; in actual engineering, whether the rock is cracked or not can be judged by comparing the theoretical value of the tensile strength with the measured value, meanwhile, the tensile strength of the rock can be predicted, and the method is simple and feasible.
2. The invention provides a method for calculating the tensile strength of a rock under confining pressure, which is a brand-new method for determining the tensile strength of the rock, wherein the tensile strength of the rock is determined in a piecewise function mode, so that the evolution rule of the tensile strength of the rock under different confining pressures is well disclosed; by the method, the tensile mechanical behavior of the rock can be more intuitively known, the tensile failure characteristics of the rock can be known, and early warning and prevention and control suggestions are provided for the tensile failure instability of the rock caused by underground engineering, slope excavation, mining and the like.
Drawings
FIG. 1 is a schematic overall flow diagram of the present invention;
FIG. 2 is a graph showing the relationship between the confining pressure and the tensile strength of granite according to an embodiment of the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, the following detailed description of the present invention is provided with reference to the accompanying drawings and specific examples.
The invention provides a method for calculating the tensile strength of a rock under confining pressure (a method for short, see figures 1-2), which comprises the following steps:
step S1, performing tensile tests on the rock sample under different confining pressure conditions, and acquiring the tensile strength of the rock sample under different confining pressure effects;
s2, performing data fitting according to different confining pressures and corresponding tensile strengths thereof, establishing a relation criterion of rock confining pressure and tensile strength as formula (1), and calculating the tensile strength of the rock according to the criterion;
wherein σ3As tensile strength, σ1Is the confining pressure value; and m, n, k, q and a are constants related to the properties of the rock materials, and the values of the constants are different for different rock materials.
Examples
The embodiment provides a method for calculating the tensile strength of a rock under a confining pressure condition, which comprises the following steps of:
step S1, performing tensile tests on the rock sample under different confining pressure conditions, and acquiring tensile strength of the rock sample under different confining pressure effects;
1-1, preparing a rock sample by adopting granite, and processing the rock sample into a cylinder with the height of 100mm and the diameter of 50 mm; the processing precision and the surface evenness of the sample accord with the national standard; two ends of the rock sample are respectively bonded with the metal end head with the threaded hole through super glue (9900 acrylic acid structural glue), and are placed for 48 hours to achieve bonding strength;
1-2, vertically installing a rock sample on a tension-compression conversion device, and fixedly connecting metal end heads at two ends of the rock sample with connecting ends at the upper part and the lower part of the tension-compression conversion device through bolts respectively; then integrally sealing the tension-compression conversion device provided with the rock sample in a confining pressure cavity of a three-axis compression testing machine, wherein two loading heads of the three-axis compression testing machine are fixedly connected with a loading end of the tension-compression conversion device respectively, filling silicone oil into the confining pressure cavity, and applying confining pressure on the rock sample by extruding the silicone oil;
the structure and the principle of the tensile-compression conversion device are disclosed in patent CN201611055843.7, and the function of the tensile-compression conversion device is to convert the compressive stress of a triaxial compression tester into tensile stress; the triaxial compression testing machine can adopt a TFD-2000L microcomputer servo control rock triaxial rheological testing machine, the axial maximum testing force of the testing machine can reach 2000kN, the maximum lateral pressure is 100Mpa, and the temperature control range is from room temperature to 200 ℃;
1-3, applying confining pressure to the rock sample, gradually applying axial pressure to the rock sample after the confining pressure value is stable, and converting the axial pressure into tensile stress by a tension-compression conversion device to realize the tensile test of the rock sample; when the rock sample breaks, stopping stretching, and measuring and recording the tensile strength of the rock sample by using a triaxial compression testing machine; changing the confining pressure value, performing a tensile test on the rock sample, repeating the test for multiple times, measuring and recording multiple groups of confining pressure values and corresponding tensile strengths by using a triaxial compression tester, wherein the results are shown in table 1;
TABLE 1 tensile Strength at different confining pressures
| Confining pressure (MPa) | Tensile Strength (MPa) |
| 0 | -7.68 |
| 3 | -8.71 |
| 6 | -8.99 |
| 9 | -8.40 |
| 12 | -6.79 |
| 15 | -7.41 |
| 18 | -6.34 |
| 20 | -4.34 |
| 21 | -4.20 |
| 24 | -2.31 |
| 28 | -1.21 |
S2, performing data fitting according to different confining pressures and corresponding tensile strengths thereof, and establishing a relation criterion of the rock confining pressure and the tensile strength as shown in a formula (1); calculating the tensile strength of the rock according to the relation criterion of the confining pressure and the tensile strength;
the test data in table 1 were fitted to obtain a tensile strength versus confining pressure curve for granite (as shown in fig. 2), and the tensile strength versus confining pressure curve for granite was found by analysis to consist of two very distinct parts: when the confining pressure level is low, the tensile strength of granite shows the change trend of a quadratic function curve along with the increase of the confining pressure; when the confining pressure level is higher, the tensile strength of granite presents a linear variation trend of a linear function along with the increase of the confining pressure, and two curves are smooth, continuous and conductive at a connecting point;
the relationship criterion of confining pressure and tensile strength, sigma, is derived from the relationship curve in fig. 2 as formula (1)3As tensile strength, σ1When the confining pressure value is obtained, m is 0.0213, n is-0.2398, k is-7.938, q is-13.936, and a is 16.77.
When the relation criterion of rock confining pressure and tensile strength is applied, a tensile test of a rock sample is required to be performed in advance according to the operations of the steps S1 and S2, and the values of m, n, k, q and a corresponding to different rock materials are determined; the relation criterion can be used for preventing rock collapse, for example, in tunnel excavation engineering, the confining pressure value of a certain rock can be obtained through measurement, and the theoretical value of the tensile strength of the certain rock in the fracture process can be obtained through calculation according to the relation criterion of the formula (1); the actual strength of the rock at the position is monitored in real time through the existing methods such as a hydraulic fracturing method, when the actual strength of the rock is smaller than a theoretical value of tensile strength, the rock is not cracked, and excavation can be continued; when the actual strength of the rock is greater than or equal to the theoretical value of the tensile strength, the rock is cracked, and the excavation operation needs to be stopped. The relation criterion can also be used for predicting the tensile strength of the rock under the conditions of small confining pressure or extra large confining pressure in a laboratory, the small confining pressure is not easy to control, the extra large confining pressure is particularly dangerous to implement and is not easy to implement, and the tensile strength of the rock under the two conditions can be directly obtained without testing by using the relation criterion.
The method carries out the same operation on the sandstone, the shale and the marble respectively, and the relation curves of the tensile strength and the confining pressure of the three rocks are obtained and all meet the following conditions: when the confining pressure level is low, the tensile strength of the rock shows a quadratic function curve change trend along with the increase of the confining pressure; when the confining pressure level is higher, the tensile strength of the rock shows a linear variation trend of a linear function along with the increase of the confining pressure, and two curves are smooth, continuous and conductive at a connecting point, namely the rock with different materials has the relation criterion.
The invention is applicable to the prior art where nothing is said.
Claims (5)
1. A method for calculating the tensile strength of a rock under confining pressure is characterized in that the method calculates the tensile strength of the rock according to the relation criterion of rock confining pressure and tensile strength of a formula (1);
wherein σ3As tensile strength, σ1Is the confining pressure value; m, n, k, q and a are constants.
2. A method of calculating the tensile strength of a rock under confining pressure as claimed in claim 1, characterized in that the method comprises the steps of:
step S1, performing tensile tests on the rock sample under different confining pressure conditions, and acquiring tensile strength of the rock sample under different confining pressure effects;
and step S2, performing data fitting according to different confining pressures and corresponding tensile strengths thereof, determining constant values related to the current rock material property in the formula (1), and calculating the tensile strength of the current rock under different confining pressure conditions according to the determined relation criterion of the rock confining pressure and the tensile strength.
3. The method for calculating the tensile strength of a rock under confining pressure according to claim 2, wherein the tensile test in step S1 is performed by:
1-1, preparing a rock sample, wherein two ends of the rock sample are respectively bonded with a metal end with a threaded hole;
1-2, vertically installing a rock sample on a tension-compression conversion device, and fixedly connecting metal end heads at two ends of the rock sample with connecting ends at the upper part and the lower part of the tension-compression conversion device; then integrally sealing the tension-compression conversion device provided with the rock sample in a confining pressure cavity of a three-axis compression testing machine, wherein two loading heads of the three-axis compression testing machine are fixedly connected with a loading end of the tension-compression conversion device respectively, and filling silicone oil into the confining pressure cavity;
1-3, applying confining pressure to the rock sample, and gradually applying axial pressure to the rock sample after the confining pressure value is stable; when the rock sample breaks, the stretching is stopped.
4. The method for calculating the tensile strength of the rock under the confining pressure condition according to claim 3, wherein the rock sample is made of granite, and the rock sample is a cylinder with the height of 100mm and the diameter of 50 mm.
5. The application of the tensile strength calculation method of the rock under the confining pressure condition is characterized in that a tensile test of a rock sample is required to be performed in advance, and values of m, n, k, q and a corresponding to different rock materials are determined; measuring the confining pressure value of a rock at a certain position, and calculating according to the relation criterion of the formula (1) to obtain the theoretical value of the tensile strength of the rock at the position when the rock is broken;
monitoring the actual strength of the rock at the position in real time, and when the actual strength of the rock is smaller than the theoretical value of the tensile strength, indicating that the rock is not cracked, and continuously excavating; when the actual strength of the rock is greater than or equal to the theoretical value of the tensile strength, the rock is cracked, and the excavation operation needs to be stopped.
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| CN112525671B (en) * | 2021-01-21 | 2021-07-30 | 东北石油大学 | Rock direct tensile test device under true triaxial confining pressure condition |
| CN113008307B (en) * | 2021-03-09 | 2021-11-30 | 华侨大学 | Method for determining fracture intervals of equal-interval fractured rock stratum |
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